How to use the discriminant to find out what type of solutions the equation has for 3x^2 - x + 2 = 0?

1 Answer
Rohan N.
Mar 26, 2018

Zero roots

Explanation:

Quadratic formula is x=(-b+-sqrt(b^2-4ac))/(2a)
or
x=-b/(2a)+-(sqrt(b^2-4ac))/(2a)

We can see that the only part that matters is +-(sqrt(b^2-4ac))/(2a)
as if this is zero then it says that only the vertex -b/(2a) lies on the x-axis

We also know that sqrt(-1) is undefined as it doesn't exist so when b^2-4ac=-ve then the function is undefined at that point showing no roots

Whilst if +-(sqrt(b^2-4ac))/(2a) does exist then we know it is being plussed and minused from the vertex showing their are two roots

Summary:
b^2-4ac=-ve then no real roots
b^2-4ac=0 one real root
b^2-4ac=+ve two real roots

So
(-1)^2-4*3*2=1-24=-23 so it has zero roots

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